Beginning with elephants, the gut retention time data from all four individuals were pooled. Seed numbers were weighted based on the number of seeds consumed by that elephant. If, e.g., elephant 1 had eaten 100 seeds, and elephant 2 had eaten 50 seeds, one seed found in elephant 1’s dung would count as one seed in the pooled data, but one seed found in elephant 2’s dung would count as 2 seeds in the pooled data. Our final gut retention curves were calculated based on the proportion of ingested seeds defecated versus time, instead of just the absolute number of seeds defecated versus time.

Using these gut retention curves, we created a cumulative distribution function (CDF) for elephant gut retention times. This CDF was used to assign gut retention times to numbers from 1 to 100. For example, if it took 42.5 hours for an elephant to defecate 50% of D. indica seeds it would deposit overall, then 42.5 was assigned to the number 50. The maximum gut retention was assigned to the number 100.

Next, 30,000 gut retention times were randomly sampled from these 100 numbers. We then needed to calculate a corresponding displacement value for each of these gut retention times. For each of the 30,000 GRTs, a displacement versus time curve was then randomly selected with replacement from the movement data (see Movement Data—Elephants) until the curve included the randomly selected gut retention time. For instance, if the randomly selected gut retention time was 72 hours, and the displacement versus time curve we selected ran only to 55 hours, another displacement versus time curve was selected.

Then, the displacement corresponding to the selected GRT in the randomly chosen curve was found by assuming the animal moved in a straight line at a constant pace between two available points. In the above example, if movement data points were available at 68 hours and 76 hours on our displacement v. time curve, we assumed that the displacement at 72 hours was the average of the displacements at 68 and 76 hours.

Once 30,000 displacement values were thus generated for elephants, the same procedure was followed for buffaloes and then cattle. The only difference was that no displacement versus time curves that started at night were utilized, since bovids were unlikely to find and consume D. indica at night. The displacements were then plotted as dispersal kernels, or seed shadows, for each species.